The Antec 300 is kind of a miserable case. For about the same price, I'd suggest this (
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119233&Tpk=HAF 912) for a little more, this (
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119197)
HDD is a 5400RPM model. You'll want 7200rpm for an OS drive (
http://www.newegg.com/Product/Product.aspx?Item=N82E16822152185) Edit: From the OP, apparently this drive has nearly the speed of a 7200RPM drive, and 2x the capacity of the drive I linked to, for like $10 more (
http://www.newegg.com/Product/Product.aspx?Item=N82E16822152245)
RAM is fine
PSU is overpowered for a single 570. If you are going to SLI, keep it. If not, you can safely drop down to the 650 model from the same series ($20 or so savings I think).
CPU is fine, but if you want to OC, a heatsink like the Hyper 212+ ($30) is recommended.
If it will fit, and you hate the noise from a stock video card, you could go up to a model like this (
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121432) or this (
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125384) for not a whole lot more money after rebate. If you don't mind that noise, the card you picked is fine (I kind of regret going for a stock GTX 580, but I got it for $330, so I can't complain).
The mobo you picked is kind of overkill. You could step that down to a $100-$150 model from Asus, Gigabyte, or ASrock, and save $50-$100. If the board has features you need though, go for it.
Other than that, everything else looks fine (I'm not the guy to talk to about monitors).